Which king of Judah had a copy built of an altar he saw in Damascus?

Answer: Ahaz

Visiting Tiglath-pileser in Damascus, Ahaz sent Uriah the priest a model of an altar he saw there, and Uriah built a copy.

“Then King Ahaz went to Damascus to meet Tiglath-pileser king of Assyria. On seeing the altar in Damascus, King Ahaz sent Uriah the priest a model of the altar and complete plans for its construction.”— 2 Kings 16:10 (BSB)